Shows the decomposition of the Jacobian matrix for fixation of a tilted surface and tangential fixation of a surface.

This decomposition uses a pinhole camera model and we assume y = 0. 1The tilt angle α is defined between the plane’s normal vector and the direction of gaze. 2In this case the plane is parallel to gaze and appears at a very small distance of x aside from the gaze. Note that in the limit, where the distance approaches zero, the derivative components approach ±infinity. 3In this case a circle is defined with the radius R at the position (X, Z) = (R, d). The discriminant is .